An elementary treatise on the differential calculus, in which the method of limits is exclusively made use of, by the Rev. M. O'Brien.

vi

PREFACE.

the Infinitesimal method; but from various circumstances I found it impossible to send the work to the
press at the time originally promised to my bookseller,
without omitting these concluding chapters. I mention
this to account for the absence of allusions to the
History of the Differential Calculus, which were all
reserved for the final chapter, and the small number
of Examples in the Appendix.
Professor Peacock's excellent collection of Examples,
which have been of such service to the Mathematical
Student, is now out of print; but Mr Gregory's work
lately published will supply its place, which contains,
not only a great number of well-selected and valuable
examples, but also many important explanations and
theorems not to be met with in any elementary treatise. In a subject of so much importance as the
present, the student ought not to confine his attention to one book or system: for a very valuable treatise
bn this subject he is referred to that published by the
Society for the Diffusion of Useful Knowledge.
In the general plan of this work, and in several
particulars, I have deviated from some of the methods
often made use of, partly in attempting to put the subject in a simpler and clearer point of view, and partly
in avoiding certain steps of reasoning which appear to
be defective. One of these is the fallacy of establishing premises on a certain implied condition, and
drawing a conclusion from them by a direct violation